This recipe by Mihl covers the first two requirements, but I'm not sure if it melts in hot chocolate because I haven't tested that myself.
As copied from the recipe itself, here are the ingredients:
For the marshmallows
- 120 ml (1/2 cup) plus 60 ml (1/4 cup) water
- 2 teaspoons agar powder
- 200 g (1 cup) sugar
- 100 g (1/3 cup) syrup (see notes above)
- 120 ml (1/2 cup) chickpea brine from a can
- 1/2 teaspoon guar gum (or xanthan)
- 1/2 teaspoon lemon juice
- 1 teaspoon vanilla extract
- 100 g (1 cup) powdered sugar
- 120 g (1 cup) corn starch
Place 120 ml (1/2 cup) of water in a small saucepan and add agar powder. Dissolve and set aside.
Combine sugar, syrup, and remaining water in another small saucepan fitted with a candy thermometer.
Bring to a boil and cook for about 6 minutes over high heat until the mixture reaches 120°C (248°F).
Bring the agar mixture to a boil, cook for one minute while stirring and remove from heat.
While the syrup is still boiling combine chickpea brine, guar gum, and lemon juice in a heatproof bowl. Beat for about two minutes, then add vanilla and beat for another two minutes or until the mixture is very stiff.
Very carefully pour the hot syrup into the chickpea brine mixture while still beating. The mixture should not deflate but stay fluffy.
Continue to beat for two minutes until everything is mixed well.
Add agar mixture and beat for another five minutes or until the bowl has cooled down. The batter should stay fluffy, and beating should produce firmer and firmer ribbons. The mixture should be stiff and keep it's shape if you remove the beaters.
Sift together powdered sugar and starch.
Dust a rectangular pan (18 x 28 cm or 7 x 11 inch - alternatively use a 8 x 8 inch square pan) with one third of the starch and sugar mixture. Make sure the whole bottom is covered.
Carefully pour the marshmallow mixture into the pan.
Let cool for two hours (at room temperature, not in the fridge!) or until set.
Cover with more starch and sugar and cut into small squares or use your favourite cookie cutter.
Generously roll in remaining powdered sugar mixture to avoid stickyness.
Place on a baking sheet and let dry for at least 24 hours. When they are dry on the outside they are ready to be store in an airtight container.